Gough suffered a broken finger while batting against South Africa at Edgbaston on Friday and will be out of action for about a month.
However, Byas declared: "We have kept winning in one-day cricket even though we have been without Darren on several occasions and I am confident that whoever comes in to replace him will do a good job.
"I am bitterly disappointed for Darren himself but I am not despondent about our chances."
Yorkshire, whose County Championship match against Leicestershire at Headingley was abandoned as a draw yesterday, hope the Australian batsman Darren Lehmann will be fit to play in today's AXA League game between the sides.
Lehmann missed the four-day encounter with a disc problem but has had an injection in a bid to speed up his recovery, and Yorkshire would like him to play a competitive match before Tuesday's semi-final.
Rain wiped out yesterday's championship action - just as it did on the first day - with Yorkshire taking nine points from the draw and Leicestershire eight.
Leicestershire were 158 runs ahead with eight second- innings wickets standing - but any hopes of a contrived finish were washed away when heavy rain returned at 1.30pm.
At Southampton, Gary Butcher, the brother of the England opener Mark Butcher, was in the thick of the action as Glamorgan battled to save their match with bottom-of-the-table Hampshire.
Butcher was caught by the wicketkeeper, Adrian Aymes, off Peter Hartley for 85. Alun Evans had earlier hit 87 before being caught behind off John Stephenson as the Welsh county were dismissed for 285 in their second innings, giving Hampshire a target of 84 runs to win off a minimum of 38 overs
Adrian Rollins fell for 107, caught by Mike Smith off Jon Lewis, as Derbyshire, who followed on 169 runs behind, progressed to 269 for five against Gloucestershire at Chesterfield. Michael May gave Rollins some sound support with 54 before he was caught behind by Jack Russell off Mark Alleyne.
The lively Lewis had earlier taken six for 48 - his best first-class figures - as the home side were skittled out for 290 in their first innings. Matthew Cassar remained unbeaten on 78 but he could not prevent Gloucestershire inviting their opponents to bat again.Reuse content